Collision detection in cycles
I dont know about the blender logic operations but this is what I can do in this case:


Add a driver for the operation you want to apply to the object.
Add a distance variable and set the object to itself and the other object.
Add a custom property and call it margin which will be the margin of the object (the distance in which the object will interact from the origin point).
Add this custom property to a single property variable.
Type "ternary conditional operator" like this in the expression.
Now when ever the "Cube.001" touch the "cube" the scale will change to 2 instead of 1 (and of course you can change the operation)